Multiparametric flow cytometry analyses provide single-cell measurements that are critical for understanding the cellular heterogeneity both within individual tumors and across tumors. Even as the cytometry technology is rapidly advancing, approaches for analyzing complex single-cell data remain inadequate. The existing cytometry data analysis approaches are often subjective and labor-intensive processes that require users' deep understanding of the underlying cellular phenotypes. This limitation has become a critical bottleneck of single-cell analysis. My long-term goal is to develop novel computational approaches to enable objective analysis of high- -dimensional single-cell data. The overall objective of this application is to develop and apply topological methods to objectively identify the cellular hierarchy underlying flow cytometry data, and infer the dysregulation of cellular hierarchy and the drug response in patients with AML. The central idea is to consider a flow cytometry dataset as a high-dimensional point cloud of cells, and use topological methods to computationally extract the shape of the cloud. Based on the preliminary data, this shape can be used to infer the phenotypic hierarchy underlying heterogeneous populations of cells. The specific aims are (1) develop methods to objectively identify the cellular hierarchy underlying individual AML samples; (2) develop methods to model the treatment responses of patients with AML using the changes in their cellular compositions. The proposed aims are expected to produce novel analytical methods for single-cell data, and provide insight into the dysregulation of differentiation and drug response in AML. The proposed research is innovative, because it views cellular heterogeneity as a continuum of phenotypic and functional changes with branchings, and aims to identify this continuum without prior knowledge of well-defined cell types. The proposed research is significant because it removes the bottleneck in the computational aspect of high-throughput single-cell analysis. The proposed research is expected to reshape the way in which cytometry data are analyzed, and promote the use of cytometry analysis to study the cellular heterogeneity in diverse fields.